Tuesday, July 28, 2020

Kiss Kiss Bang Bang

    To mark the 10th anniversary of the Common Core's publication, here are my capsule-length reviews of selected K-8 standards:
(All reviews stolen from movie listings posted daily in The New York Times.)

By the end of Grade 3, know from memory all products of two one-digit numbers.
 Curiously retrograde

Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.  For example, which of the following equations are true and which are false?  
6 = 6,  7 = 8 - 1,  5 + 2 = 2 + 5,  4 + 1 = 5 + 2 
 Top notch existential confusion

Understand that attributes belonging to a category of two-dimensional figures also belongs to all subcategories of that category.  For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
 Laborious brainteaser

Develop a probability model (which may not be uniform) by observing frequencies in the data generated from a chance process.  For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down.  Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?
 Predictable but hard to hate 

Find all factor pairs for a whole number in the range 1-100.  Recognize that a whole number is a multiple of each of its factors.  Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number.  Determine whether a given whole number in the range 1-100 is prime or composite. 
 Disaster by the numbers

Analyze and solve pairs of simultaneous equations.
Zoom, crash, repeat

 Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number.  If p and q are integers, then -(p/q) = (-p)/q = p/(-q).  Interpret quotients of rational numbers by describing real-world contexts. 
 Almost willful lack of fun

Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. 
 Answers questions no one needed to ask

Use place value understanding to round multi-digit whole numbers to any place.
 Blunt and sadistic

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.  For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3.  (In general (a/b) ÷ (c/d) = ad/bc.)  How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally?  How many 3/4-cup servings are in 2/3 of a cup of yogurt?  How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
 Overstuffed spectacle

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies using $ and ¢ symbols appropriately.  For example, if you have 2 dimes and 3 pennies, how many cents do you have?
 Melancholy melodrama
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch.  Show the data by making a line plot where the horizontal scale is marked off in appropriate units--whole numbers, halves, or quarters.
 Best when no one's talking 

Solve multi-step real life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically.  Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.  For example, if a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50.  If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches for each edge; this estimate can be used as a check on the exact computation.
 Turgid schedule filler

Fluently multiply multi-digit whole numbers using the standard algorithm.
 Incredibly tedious

Fluently add and subtract multi-digit whole numbers using the standard algorithm.
 Strictly formulaic

Solve unit rate problems including those involving unit pricing and constant speed.  For example, if it took 7 hours to mow 4 lawns, then at that rate how many lawns could be mowed in 35 hours?  At what rate were lawns being mowed?
 Hack work
Model shapes in the world by building shapes from components (i.e. sticks and clay balls) and drawing shapes.
 Broad, freewheeling fun


Wednesday, July 15, 2020

A Requiem For Twitter Math Camp

    Five years ago this month I boarded a plane in Newark, NJ and, after a layover in San Francisco, flew into the small airport in Ontario, CA.  I had traveled across the country to attend something called Twitter Math Camp, which in the summer of 2015 was being held on the campus of Harvey Mudd College in Claremont, CA.  It was difficult to explain to my family, friends and co-workers exactly what it was, or what I was going to be doing there, because I didn't really know myself.  Was it a camp?  Was it a conference?  What does twitter have to do with it?  How is it all organized?  What I did know was that I was going to get to see some of the MTBoS people who had inspired me to explore new ways to teach math and who had supported and encouraged my attempts to blog about my experiences.  I had never met any of them, and was more than a little apprehensive about what they would be like in person, and how welcoming the community in general would be.  I had struck up an online friendship with Graham Fletcher, and he agreed to share a room with me and split what turned out to be a very small rental car.  He was standing outside the terminal when I walked out with my bag, and we recognized each other immediately.  I reached out my hand, but he shook his head, opened his arms, and gave me a giant bear hug that nearly crushed me to death.  
     TMC '15 was everything I could have hoped for, and much, much more.  Beyond the amazing sessions, it was an opportunity to meet people from all over the country, all over the world, actually.  People who were involved in math education in all kinds of different ways: elementary school teachers and district administrators, university professors and math coaches; private school, public school and home school; urban, suburban, rural; big, small, and in between.  We were all there, on our own time and on our own dime, because we were passionate about what we did and eager to learn from each other.  During the day we went to sessions, interspersed with keynotes and quick hit "My Favorites".   After, we hung out in the courtyard of the hotel till all hours of the night.  I couldn't sleep, my head was spinning at 100 miles per hour.  I kept Graham up all night, blabbering away non-stop about who I had met, what we had talked about and what I was going to do when I got back to the world.  He told me I was drinking from a firehose.  He also told me to stop talking and go back to sleep.  By Sunday morning's final assembly I was emotionally exhausted.  When a group of participants stood up and sang a goodbye song, I started to tear up.  And when Lisa Henry announced the date and location of next year's TMC, I immediately phoned my wife and told her to block it out on the calendar.
     When I got back home everyone asked: "What was it like?"  
     All I could think of was something that Christopher Danielson had said: "It's like being in the faculty lounge of your dreams."  Like baseball fantasy camp, except with math teachers.  

      I went back to Twitter Math Camp in 2016, 2017, and 2018.  Each time I was afraid that the magic would be gone, that I would be disappointed, that it wouldn't live up to my expectations.  Each time I was wrong.  Part of it was the different locations--it was fun to explore a new city each summer.  Part of it was reconnecting with old friends.  Part was the fact that each time I went back I connected with new people, widening my network of friends and colleagues, which made our virtual interactions during the rest of the year richer.  Part of it was my own increasing confidence presenting sessions.  Although I knew that attendance was capped and I wasn't guaranteed a spot, I began to count on it to recharge my batteries for the coming school year. 
     More than the venues, more than the cities, more than the sessions, more than the keynotes, more than the math, for me TMC was a place where, for four brief days, 200 lives intersected in a very intimate way.  Shared breakfasts, lunches, and dinners.  Early morning coffees and late nights in hotel courtyards and lobbies and, on one special occasion, in a college dorm.  Clusters in the corners of classrooms.  On stairwells and in hallways, on Ubers and in airports.  I couldn't even begin to count all the different conversations I had with all the different people I met along the way.  They challenged me, informed me, encouraged me.  They agreed and pushed back.  They listened, and no matter how crazy I sounded they made me feel like I had something worthwhile to say.  For me, it was different than the big, industrial NCTM conferences.  Nobody was selling anything, nobody was angling for a deal or working the room, or trying to impress anybody.  It wasn't institutional.  It was t-shirts and shorts.  It was, as we would say in Yiddish, haimish.
     In 2018 I convinced a former work colleague to join me.  Now I was the old hand and she was the nervous newbie.  I was curious to see her reaction and to look at something I had begun to take for granted through her eyes.  How would she would find the experience?  I told her that I'd always be around for her, that I wouldn't leave her without someone to have breakfast, lunch, or dinner with, or to hang out with after the day's sessions were through.  There had been talk that things had gotten cliquey, that newcomers weren't being made to feel especially welcome.  I knew that people experienced TMC in different ways, and that the leadership had made attempts to make people feel more included.  I knew that not everyone felt the same way about it that I did.  Turns out I had nothing to worry about: after the first day she had met a bunch of people and made her own friends, some of whom became my new friends.  She talked about going back.  I started making plans with Brian Miller to submit a proposal to co-present a session at TMC '19 in Berkeley.

      I didn't see it coming.  One day the acceptances came out, and then, suddenly, it imploded.   I've worked through the stages of grief, and I think I've finally arrived at acceptance.  Looking back these last few weeks at my pictures, revisiting the archives and the old tweets, my heart is filled with gratitude for all those who worked so hard to make it happen.  I'm sorry if I didn't let you know just how thankful I am.  I know I was blessed to be able to experience those 16 special days in the summers of 2015, 2016, 2017, and 2018.  It's not my intention to reopen any wounds or reignite any debates.   It's just I never got the chance to say goodbye.



Wednesday, July 1, 2020

And Then They Came For the Statisticians

ORLANDO, Fla. (AP) -- The world's largest statisticians group added to a chorus of criticism this week against the recent hiring of two political appointees at the U.S. Census Bureau.  The American Statistical Association says the appointments earlier this week of Nathan Cogley and Adam Korzeniewski to top posts even though they have little experience at the agency "are in direct conflict with the bureau's mission to ensure proper, accurate, and timely delivery of statistical information to the public." Cogley is a political science professor who wrote a series of opinion pieces against the impeachment of Donald Trump.  Korzeniewski is a former campaign consultant to the pro-Trump YouTube personality known as "Joey Salads."

Mike Schneider
Associated Press
June 26, 2020 


...the suppression of its findings and the murder of those who organized it was nothing less than the obliteration of the capacity for self-analysis.  An authoritarian society, however, that is unable to form an idea of itself, whatever social engineering its leadership may have in mind, is doomed to the blind exercise of state violence.

Karl Schlögel 

     For one 24 hour period, from midnight January 6, 1937 to the following midnight, life in the entire breadth of the Soviet Union, one-sixth of the world, came to a stop.  On that day, after weeks of extensive training, one million enumerators (census takers) with a list of fourteen questions spread out over the entire country.  Their mission was to collect the information that, when analyzed and pieced together, would form a detailed picture of what Soviet society looked like twenty years after the Bolshevik Revolution.  The enumerators knocked on the doors of apartment blocks in Moscow, skied across the Arctic tundra to remote villages, and rode with passengers on the Trans-Siberian Express.  As Karl Schlögel describes in his book Moscow 1937:   

     Whether in the cities or on a river steamer, in a yurt in Kazakhstan or in a hotel in Leningrad... from different districts of the capital, from the capitals of the republics, from Kiev, from Ashbagat, from the Taiga and the Pacific ports, from the newly built suburbs.  The armada of enumerators ...not only penetrated the furthest corners of the Soviet Union; it systematically explored the social landscape...(and) discovered a Soviet Union in miniature.
     The populace was ready.  The census protocol had been highly publicized in workplaces and shops and over state media outlets.  The questions submitted to the Party leadership by the Census Board were edited by Party leader and supreme ruler of the USSR Joseph Stalin personally (he had removed eight and added one) and had been released in advance so citizens knew exactly what to expect when an enumerator showed up on their doorstep.  It was a remarkable achievement, one that required careful planning, tremendous resources and a nationwide mobilization.  What makes it even more astonishing is that, according to Schlögel, historians and demographers with access to the formerly suppressed results--made available in the 1990s after the Soviet Union's collapse--have calculated the margin of error at a low 0.5 to 0.6 percent.  
Information poster

It was Stalin who had ordered the census, and he had a lot riding on its outcome.  It had been eleven years since the last one, a time of rapid industrialization and societal upheaval.  A program of forced agricultural collectivization and two Five-Year Plans had run their course.  Stalin believed that the demographic figures would prove that the Soviet Union had built a vibrant, happy and healthy society.  High growth rates were predicted, outstripping those of rival capitalist countries.  Officially, a population figure of 170-172 million was expected (a number extrapolated from the 1926 census); Stalin was hoping for something closer to 180 million. 

Census data being processed
     They knew they were in trouble almost immediately.  Preliminary results indicated that average growth, while surpassing Germany, England, and France, was exceeded by both the United States and Japan.  Stalin's added question was about religious affiliation; he expected the state's anti-religion policies to reflect a high number of non-believers.  Yet close to 60% of the adult population identified themselves as believers.  Most alarming, the final count would be somewhere around 162 million, 8 million people shy of the official pronouncement.  I.A. Kraval, the Census Bureau Chief, ordered a recount, but only several thousand unenumerated persons were found.  In late January, the provisional results were presented to the Party leadership, and a further report in March confirmed the original figures.  Kraval and his team of demographers and statisticians, fighting for what they knew were their lives,  did their best to excuse the results, but the difference between the final count and the publicly stated number of 170 million was too great to explain away.
     Where were the missing 8 million?  And who was to blame?  The biggest discrepancies between the expected numbers and the actual count were in the regions hardest hit by the devastating 1932-1933 famine caused by Stalin's policy of forced collectivization.   Historians are still debating the actual death toll--estimates range up to 7 million--and also to what extent anyone at the time had an accurate fatality count.  (Ironically Kraval was sending false reports to Stalin, downplaying the numbers.)  In any case, the famine had been officially denied, and anyone who talked about it risked imprisonment and death.  The census data, which reflected the tragic consequences of Stalin's policy, had to be suppressed.  So did those involved with the data collection.  
     The arrests began in March.  No one was safe; from the members of the central Census Bureau to the chiefs of the regional census centers, right down to administrators at the local level.  Statisticians assigned to replace the imprisoned were soon imprisoned themselves. The statisticians and demographers were accused of sabotage and "wrecking", and labeled "Trotskyite-Bukharinite spies" and "enemies of the people".  Many of those imprisoned were eventually executed.  Kraval himself was condemned to death in August and shot.  A new census was planned for 1939.  Schlögel links this to the Great Terror:  

...having destroyed the analytical matrix which disclosed the contours of the nation and its people, and having sacrificed the very instrument that would enable them to interpret these things, the leadership... (was) overcome by a blind flight into terror, an intensification of violence whose excesses would surpass the very disasters that the census had just diagnosed.  As a result, for the catastrophe that followed there were no longer any instruments that might have diagnosed what was to come.     

      Not surprisingly, the new census resulted in a population count of 170.6 million people.  Just what Stalin had ordered.  The question about religious affiliation was eliminated.  There would not be another census until 1959.      

     Suppression of truth and truth-tellers isn't exclusive to the former Soviet Union.  It's not hard to come up with examples of our own.  The data linking smoking to cancer and the cover-up of abuses by clergy in the Catholic Church are two that come to mind.  We know stories of individual whistleblowers coming to bad ends (see Karen Silkwood) and we also know of consumer advocates forcing changes to promote public safety (see Ralph Nader).  Thankfully, we have avenues to access information, mechanisms to uncover truths, protections for those who would speak truth to power and independent media outlets to publicize those truths that would be unthinkable in the Soviet Union under Stalin.  Our system of government is based on checks and balances, and while it may not always work the way we want it to, it does provide a measure of protection against the worst autocratic tendencies of an executive, protections that, again, would have been unthinkable to Stalin.
     Consider the case of our census, currently in progress.  When the Trump administration tried to add a question related to citizenship, it was met with resistance and criticism, not only from progressives, but from statisticians and demographers, who argued it would threaten its integrity, estimating that inclusion of the question could lead to an undercount of 9 million people.  The pretext for adding the question was seen as strictly political; it was a way to depress the count in heavily Democratic areas, which would have consequences for proportional representation in Congress, how many electoral votes a state receives, and how and where some $1.5 trillion in federal money is allocated. A lawsuit challenging the question made its way to the Supreme Court.  In a fractured and complicated 5-4 decision, the court ruled that the justification for adding the question was invalid.  Unable to delay the implementation of the constitutionally mandated decennial census, the administration threw in the towel.  
     However the recent appointments of Cogley, a frequent radio commentator and former head of the department of government, legal studies and philosophy at Tarleton State University and Korzeniewski, who once worked as a consultant for the failed Staten Island congressional run of Joey "Joey Salads" Saladino, a YouTuber famous for racist pranks, and whose primary qualification seems to have been that he once worked in a census bureau field office, to top positions at the U.S. Census Bureau should be cause for alarm.  It certainly is to Kenneth Prewitt, a former Bureau director.  "These are two people ill equipped to actually manage the census," he said in a Politico report:
They're very well equipped to advance political interests, especially those of the Republican Party.  That's their background and their career goals.  It's unprecedented for two political appointees to be added to the bureau in the middle of a census count in the recent history of the Census Bureau.

     What influence will they exert on the counting and reporting of the census figures?  Will they be guided by best statistical and demographic practices?  Do they even know (or care) what those practices are?  Were they put there to do the bidding of the administration that appointed them?  Will the final census be an accurate reflection of America in the year 2020?  And if it isn't, will we even know?

    All this is to say that our community has a very important role to play.  Math helps build the models, math looks at the data, math runs the statistical analysis.  It's our job to call bullshit when we see it...

...and it's our job to give our students not only the tools they need to be discriminating and critical consumers of information, but the confidence to use their voices to speak out when they see data being used to deliberately manipulate and confuse; whether it's related to: 
something as innocuous, like how many people attend an inauguration, 
something important, like a census count, 
something serious, like the death toll from the coronavirus, or 
something that threatens the very existence of life on the planet, like climate change.  
So whether you're in kindergarten teaching kids how to count with one-to one correspondence or in high school teaching AP Stats, or anywhere else above, below, in between or sideways, please keep your shoulder to the wheel.